Design of motion capture system-aided lower limb exoskeleton

Abstract

This paper develops a human lower limb exoskeleton device combining kinematics, vibration, biomechanics, and a machine vision motion capture system that can replicate the physiological structure of human lower limbs, accurately and automatically follow the user’s movements, and assist the human body in weight-bearing walking. First, the visual environment is constructed and calibrated with 36 reflective marking balls using the CAST marker set method. The maximum error is 0.893 mm, indicating that the accuracy of the system is submillimeter. The maximum difference between the kinematic simulation and the experiment is 34.8% on the Y axis and 13.9% on the Z axis, both of which indicate good agreement. Then, finite element modeling is used to analyze the human lower limb exoskeleton in its standing phase and the equivalent position of the legs. The results showed that the corresponding force value of both legs’ support is the largest, being 51.8% of the 6061-T6 yield strength and thus meeting the strength requirements. The first-order intrinsic frequencies are 18.239 and 23.086 Hz for the standing phase and the leg brace phase, respectively. This indicates that the human lower limb exoskeleton does not resonate with the motor during walking. Walking experiments are conducted on subjects wearing a 20 kg load. The maximum booster effect occurs in the right thigh of the subjects, and the variation range of EMG amplitude of subjects wearing the human lower limb exoskeleton is 15.5% of that when not wearing it. The above results show that the exoskeleton assists the human body and can automatically follow the human body when walking.

Introduction

There is a large variety of human exoskeletons, and it is common for them to be offset from the center of the corresponding human joints during use. This can cause some discomfort to the wearer and even cause damage to the human body after overuse. In order to amplify the impact of this problem, this paper uses a load-bearing exoskeleton for experimentation. Load-bearing exoskeleton is a wearable device designed to reduce human weight, enhance physical strength and labor capacity, and has broad prospects in the military and industrial fields. Yuan et al., ¹ proposed a hand tracking system utilizing a motion camera and ArUco markers to measure hand joint movement angles. Three joint angle estimation methods were proposed: position-based, orientation-x-based, and azimuthal pad-based. The results demonstrated that the azimuthal pad-based method performed more consistently and efficiently under multi-camera conditions than the others. Malhan et al. ² proposed a method for 3D reconstruction using a low-cost depth camera mounted on a commonly used industrial robot. Technological advances such as camera calibration, point cloud capture cycle reduction, and uncertainty estimation have enabled 3D reconstruction with sub-millimeter accuracy. Su et al. ³ used four hydraulic cylinders to drive hip and knee joints with a design load of 50 kg; the kinematics and dynamics were subsequently modeled and analyzed and then validated by simulations, after which the problems related to exoskeleton stability, load-carrying capacity, tracking effectiveness, and durability were addressed. Liu et al. ⁴ proposed a vision-assisted autonomous lower limb exoskeleton robot to address the difficulty of patient gait transfer in complex ground environments. An autonomous gait planning method was developed based on the principles of visual feedback and motion decision-making. Adjusting the gait parameters according to environmental characteristics and safety constraints significantly improved the robot’s ability to adapt to complex environments. Liu et al. ⁵ designed a brain-controlled lower limb rehabilitation exoskeleton. A feature extraction model based on an electroencephalogram (EEG), which is a graphical record of the electrical activity in the brain, was established using wavelet transform analysis, and several control methods were explored and experimentally verified, including EEG control, preprogrammed control, feedback-based control, and neural network-based control. The rationality of the proposed design and the effectiveness of the exoskeleton were verified through mathematical modeling, virtual prototyping, and physical verification. Wang and Yin ⁶ proposed an online balanced gait generation strategy for lower limb rehabilitation exoskeleton. Online balanced gait regulation using a proportional-integral-derivative controller ensured zero maximum moment point (ZMP) stability. The simulation results validated the effectiveness of the proposed strategy in terms of gait learning and ZMP stability. Zhang et al. ⁷ used a nut-screw actuation mechanism, and the Denavit–Hartenberg and Kane methods were employed to model the kinematics and dynamics and analyze the workspace and control strategies. In addition, a dual closed-loop control strategy was proposed to ensure accuracy, and its effectiveness was verified through prototype gait control and patient experiments; the experimental results demonstrated the ability of patients to achieve stable and smooth walking. Wang et al. ⁸ studied the metabolic cost of traditional non-powered lower limb exoskeletons during sitting down and standing up, and they proposed an innovative, non-powered lower limb exoskeleton design that determined the location and stiffness of energy storage elements through muscle contribution and joint stiffness. Their results could provide a theoretical basis for the design optimization of non-powered lower limb exoskeletons. Gao et al. ⁹ focused on the challenges in patient gait planning and control strategies for lower limb exoskeleton rehabilitation robots with multimodal and robust control schemes to enhance patient engagement. An improved adaptive particle swarm optimization impedance control algorithm and a dual radial basis function (RBF) neural network-based adaptive sliding mode controller were introduced, and their effectiveness in healthy subjects was subsequently validated. Ren et al. ¹⁰ proposed a fast parameterized dynamic motion planning system able to adapt to different application requirements by adjusting a small number of parameters. In addition, an inverted pendulum model was used to ensure the fore-and-aft stability of a robot, and inverse kinematics were used to determine the robot’s end position and joint angles. Bijalwan et al. ¹¹ used Kinect sensors and inertial measurement units (IMUs) to estimate joint angles and obtain the gait profiles of lower limb joints. The results showed a sinusoidal motion of the hip and a negative correlation between ankle and knee motions. Furthermore, Mehr et al. ¹² developed an integrated control strategy, where a linear inverted pendulum flywheel model was replaced by a divergent component of the motion analytical model. Moreover, the challenges of gait trajectory planning and attitude stabilization were addressed. Yu et al. ¹³ solved the problem of a smooth transition of a lower limb exoskeleton during a robot’s walking on different terrains using a variational autoencoder (VAE), which is a generative model that can learn potential representations of input data by combining the concepts of deep learning with probabilistic graphical models, and employing reinforcement learning methods. Furthermore, the predictions of gait trajectories and events were obtained through the VAE reconstruction to minimize prediction errors. The experimental results demonstrated that the proposed method could outperform the conventional methods in the gait trajectory and event prediction tasks in the transition phase. The adjustable knee mechanism developed by Olinski et al. ¹⁴ incorporates a four-link mechanism with two motor-driven degrees of freedom to adjust the rotation position’s center. The simulation results showed that the relative error of the kinematic trajectory calculation of the rotary axis was less than 0.07%. Awad et al. ¹⁵ applied a three-PRR planar parallel mechanism to an elbow exoskeleton. The test results indicated that the exoskeleton actuation center’s movement was not optimal in certain directions during arm flexion and extension processes due to the elastic effects of the skin tissue.

Motion capture technology plays a key role in addressing the challenges in exoskeleton control due to its high accuracy and real-time nature. By accurately capturing a user’s movement intentions and action parameters, motion capture systems provide important data to support the design and control of exoskeletons. Vitali et al. ¹⁶ proposed a motion capture method that combines low-cost sensors and convolutional neural networks to address the challenges of high-precision motion tracking. The above method successfully recognized small movements and incorrect postures by integrating data from infrared sensors and RGB cameras. Liu et al. ⁴ developed a vision-assisted autonomous lower limb exoskeleton robot to improve the safety and adaptability of patients when walking. An RGB-D camera was used to acquire environmental information for autonomous gait pattern planning, and the effectiveness of the proposed robot in an indoor environment with limited obstacles was successfully verified. Zhou et al. ¹⁷ proposed an inertial motion capture system (InMoDT) for the human motion digital twin. The InMoDT achieved an average root mean square error of 4.7° in estimating orientation, with a correlation of 92.5% and a consistency of 97.8% compared to the optical motion capture system. Moreover, the InMoDT has demonstrated outstanding capabilities in human motion monitoring and estimation, as well as human-machine teleoperation. Reimer et al. ¹⁸ investigated the application of three-dimensional (3D) motion capture frameworks in the fields of sports, health, and medicine. The joint angles of the Apple ARKit and Vicon systems were compared across eight bodyweight exercises. Qiu et al. ¹⁹ introduced a lightweight and low-cost wireless inertial motion capture system for reconstructing human postures and displacements. This system is based on a human sensor network with 15 sensor nodes distributed on key human limbs. In addition, the foot displacement is calculated by initial sensor alignment and zero velocity update algorithms, and human posture is updated by fusing sensor data by the gradient descent method. The proposed 3D reconstruction method combines a human posture and a foot trajectory for simultaneous reconstruction. Gao et al. ²⁰ introduced an innovative kinematic identification method for tandem robots based on a recursive motion capture system. In this method, a motion capture system is used to recognize and track markers on a robot’s joints to acquire 3D coordinates in continuous motion. Moreover, the joint axis vectors and DH parameters are reconstructed using the optimization method. The experimental results confirmed the efficiency and accuracy of the proposed method on a six-joint robot, demonstrating that the proposed method could achieve a recognition accuracy close to that of a laser tracker. Kim et al. ²¹ proposed a system for real-time tracking of dynamic human motion that employs multiple depth sensors (e.g. Microsoft Kinect) without requiring external markers. In this system, the coordinate system of multi-sensor data is unified by an iterative nearest-point method, and a pose reconstruction method is employed to optimize the joint positions and ensure consistent motion generation. Ziegler et al. ²² analyzed human motion using a real human model and optimized the model parameters with motion data to generate 3D human trajectories. In addition, an integrated approach was proposed to identify a lower limb’s geometric parameters and gait trajectories simultaneously to describe physiologically compatible movements continuously. The above-mentioned methods consider the joint range of motion limitations and are robust to marker occlusion and system failures. Further, subject-specific movement patterns at specific speeds were derived from multiple gait cycle analyses, allowing for motion analysis, evaluation, and synthesis for simulation and trajectory planning of rehabilitation and exoskeleton systems. Ibrayev et al. ²³ proposed an advanced synthesis method to solve the problems of high cost, complex control, and bulky structures in conventional lower limb exoskeleton designs. A lower limb exoskeleton mechanism containing only six links was successfully designed through multi-criteria optimization of the mathematical model to fit the human anatomy. Wang et al. ²⁴ focused on the environmental perception of exoskeleton robots and used visual sensors and control systems to enhance their stability and safety in complex environments. Moreover, the problem of enhancing the autonomous perception of exoskeletons and the interaction between human and machine environments was solved. Wei et al. ²⁵ developed a synergy-based robot controller that generates motion patterns of the assisting leg by capturing motion information and biosignals from a healthy leg. In addition, they modeled joint stiffness estimation and human skill transfer using surface EMG signals. Furthermore, adaptive fuzzy approximators were developed to estimate the dynamic parameters of a robot and to track the reference trajectory. Martinez et al. ²⁶ simulated a viscous flow field acting on the joints of a ground-based lower limb exoskeleton and proposed a control method used to control the lower extremity exoskeleton joints on the ground. Compared to the potential field controllers, velocity controllers can significantly reduce guidance errors and a user’s sense of interference. In light of this, Zheng et al. ²⁷ combined deep reinforcement learning with sensitivity amplification control to address the problem of model parameter uncertainty and human-exoskeleton interaction dynamic challenges. A multi-body simulation environment and a hybrid inverse-forward dynamics simulation method were developed to train control strategies safely and efficiently by optimizing sensitivity tuning through the Markov decision processes.

In summary, an accurate measurement of the joint center position represents a prerequisite for exoskeleton design. Despite the variety of measurement techniques, they are all subjected to errors. However, the gait analysis can help with joint alignment. To this end, this paper collects the center coordinates of lower limb joints and gait data using machine vision and establishes theoretical models and entities using the collected data. In addition, finite element modeling and stiffness, strength, and vibration analysis are conducted on the kinematic and dynamic parameters of the theoretical model. A weight-bearing walking experiment is conducted to compare the EMG signals of subjects with and without wearing exoskeletons. This study combines kinematics, vibration, biomechanics, and a machine vision motion capture system, thereby allowing design and control strategies to be optimized for each user.

HGD acquisition

In this part, a motion capture system is used to collect the subjects’ motion images, and the three-dimensional coordinates of the centers of the lower limb joints are obtained through data processing software. On the one hand, these three-dimensional coordinates are used to determine the length of the lower limb segments of the human body as the size of the HLLE; on the other hand, they are combined with the force platform data to calculate parameters such as the motion torque, joint angle, angular velocity, and angular acceleration of each joint of the lower limbs. By analyzing these data, we can understand the movement patterns of the subjects and provide a basis for the design of the control system and joint mechanical structure of the HLLE.

As shown in Figure 1, the motion capture system consisted of nine A12 cameras, two Kistler force tables (KFT), and QTM parsing software. The A12 camera parameters were set, as shown in Table 1, operating in the standard mode with a frame rate of 100 fps. The force gauge sampling frequency was 2000 Hz.

Figure 1.

Picture of the motion capture system environment.

Table 1.

A12 technical parameters.

Mode	Pixels (MP)	Resolution	Framerate (fps)	Measuringdistance (m)	Field of view (°)
					Standard	Wide-angle	Narrow-angle
Standard mode	12	4096 × 3072	300	40	54 × 42	70 × 56	31 × 24
Normal mode	3	2048 × 1536	1040	1040

Prior to the experiment, the camera and the force table needed to be calibrated. Reflective marker balls were attached to the two calibration rods. The camera captured the infrared light reflected from the marker ball to determine the ball’s location. The L- and T-type calibration rods (i.e. LTCR and TTCR) were used to calibrate the nine cameras in the scene. The QTM software was used to connect all the cameras to the stage. The right-angled side and vertex of the L-shaped calibration bar coincided with the side and vertex of the force table, respectively, and were placed horizontally on the ground. The position of the coordinate system origin of the motion capture system was the right-angle vertex of the L-shaped calibration bar. The QTM software performed the camera calibration after the T-shaped calibration bar was moved within the field of view of the camera for 15–30 s. As shown in Table 2, among all the cameras, camera No. 5 had the smallest reprojection error of 0.600 mm, and camera No. 1 had the largest reprojection error of 0.893 mm. This demonstrated that the nine cameras could achieve sub-pixel level localization within the field of view. In addition, to calibrate the ergometer table, the subject was weighed standing on it, and the weight was measured to be 83 kg. The QTM software processed the subject’s weight to ensure that the measured weight values were located at the zero point of the coordinates.

Table 2.

Camera calibration results.

Cameranumber	Reprojectionerror (mm)
1	0.893
2	0.822
3	0.823
4	0.685
5	0.600
6	0.789
7	0.683
8	0.757
9	0.859

When selecting the marker positions in the CAST marker set, the obvious landmarks of the bones and the rotation centers of the joints are determined as reference points based mainly on the anatomical structure and kinematic principles of the human body. At the same time, the marker ball should be attached to the surface of the bone or close to the bone as much as possible to reduce the impact of soft tissue movement and deformation on the position of the marker ball and avoid the generation of soft tissue artifacts. In this way, the CAST marker set is able to provide accurate and reliable motion data capture.

The HLLE in this article is customized for a single subject. The subject in the experiment was a 28-year-old normal male with good physical health and no movement disorders.

As shown in Figure 2, the data were collected for the static standing posture and during the walking process. The data on the static standing posture were mainly used to analyze the LLJC’s position. In contrast, the data collected during walking were used to analyze the change rules of the angle, angular velocity, and moment of the LLJC. The two examined scenarios were as follows:

1. In accordance with the CAST marking set method, a total of 36 reflective marking balls were used, which were affixed to the subject’s lower body surface. The schematic diagram of marking balls on the front side of the body is shown in Figure 2(a).

2. There were four marking balls on the back of the body, as shown in Figure 2(b).

3. As shown in Figure 2(c), the subject stood and remained stationary on the force platform, and this state was maintained for 40 s. The subject’s body was then placed in a position where the force was measured by the force platform.

4. To study the differences in gait parameters at different speeds, as shown in Figure 2(d), the subject walked across the blue walkway; the walking speed varied, and it was ${\mathrm{v}}_1=0.914\mathrm{m}/\mathrm{s}$ , ${\mathrm{v}}_2=1.065\mathrm{m}/\mathrm{s}$ , ${\mathrm{v}}_3=1.147\mathrm{m}/\mathrm{s}$ , and ${\mathrm{v}}_4=0.944\mathrm{m}/\mathrm{s}$ .

Figure 2

Position marking and gait experiment: (a) front marking, (b) back marking, (c) standing, and (d) walking.

The exact names marking the locations of the balls are given in Table 3. TH1, TH2, TH3, and TH4, all in the thigh, and SK1, SK2, SK3, and SK4, all in the calf, were fixed together using a tracking plate to reduce the impact of the ball’s displacement on the skin.

Table 3.

CAST mark point set positions.

Tag name	Placement	Tag name	Setting position
L_IAS	Left anterior superioriliac spine	R_IAS	Right anterior superior iliac spine
L_IPS	Left posterior superior iliac spine	R_IPS	Right posterior superior iliac spine
L_TH1-4	Left thigh marker cluster	R_TH1-4	Right thigh marker cluster
L_FLE	Left lateral epicondyle	R_FLE	Right lateral epicondyle
L_FME	Left medial epicondyle	R_FME	Right medial epicondyle
L_SK1-4	Left lower leg marker cluster	R_SK1-4	Right lower leg marker cluster
L_FAL	Left lateral ankle prominence	R_FAL	Right lateral ankle protrusion
L_TAM	Left medial ankle prominence	R_TAM	Right medial ankle protrusion
L_FCC	Lateral aspect of the Achilles tendonstopping at the left heel	R_FCC	Lateral aspect of the Achilles tendon stopping at the right heel
L_FM5	Dorsal border of the fifth metatarsalhead of the left foot	R_FM5	Dorsal border of the fifth metatarsal head of the right foot
L_FM2	Dorsal border of the secondmetatarsal head of the left foot	R_FM2	Dorsal border of the second metatarsal head of the right foot
L_FM1	Dorsal border of the first metatarsalhead of the left foot	R_FM1	Dorsal border of the first metatarsal head of the right foot

LLJC location extraction and HGD analysis

This section explains the processes of the LLJC location extraction and HGD analysis.

LLJC location extraction

Thirty-one frames were extracted from the data on the stationary standing pose for analysis. Each frame contained the 3D coordinates of the hip, knee, and ankle joints. The mean and standard deviation values of the coordinates of each joint center point on the X, Y, and Z axes were determined, and the results are shown in Table 4. As presented in Table 4, the standard deviation’s fluctuations were very small, and the mean values of the coordinates of the individual joint centers could be used as their 3D coordinates. The results were as follows: left hip joint center coordinates were LHJC (−570.772, 222.497, 917.072), the left knee joint center coordinates were LKJC (−553.388, 278.978, 506.826), the left ankle joint center coordinates were LAJC (−533.641, 305.402, 69.849), the right hip joint center coordinates were RHJC (−779.996, 228.800, 915.793), right knee center coordinates were RKJC (−806.601, 278.627, 504.487), and right ankle center coordinates were RAJC (−829.260, 298.288, 71.245).

Table 4.

Mean and standard deviation values of the 3D coordinates of the LLJC.

Coordinate axis	X (mm)		Y (mm)		Z (mm)
	Mean	Standard deviation	Mean	Standard deviation	Mean	Standard deviation
LHJC	−570.772	0.091	222.497	0.082	917.072	0.023
LKJC	−553.388	0.069	278.978	0.027	506.826	0.013
LAJC	−533.641	0.017	305.420	0.014	69.849	0.013
RHJC	−779.996	0.091	228.800	0.066	915.793	0.013
RKJC	−806.601	0.036	278.627	0.050	504.487	0.025
RAJC	−829.260	0.015	298.288	0.008	71.245	0.013

Using the LLJC’s 3D coordinate points, the lengths of the left and right sides of the thigh and the length of the shank were obtained. The 3D distance from the left hip center to the right hip center was also obtained, as shown in Figure 3.

Figure 3.

Dimensions of the lower limb segments.

The calculation results showed that the right thigh was 0.685 mm longer than the left thigh, the left shank was 3.941 mm longer than the right shank, and the total length of the left lower limb was 3.256 mm longer than the right lower limb. Since the difference in the lower limb length from zero to 18 mm, it had no effect on the gait. The right leg size was selected as a more appropriate exoskeleton size to make the exoskeleton compact and avoid severe collisions with the ground during walking.

HGD analysis

During walking, each joint of the lower limb of the human body undergoes angular changes in the coronal, horizontal, and sagittal planes. Furthermore, the motion range of each joint is the largest in the sagittal plane, while the motion ranges in the coronal and horizontal planes are relatively small. Therefore, it was most meaningful to analyze data on changes in the angles, angular velocities, and moments in the sagittal plane.

A comparison of gait data collected at different speeds revealed that the faster the walking speed was, the greater the joint mobility, angular velocity, and output moment were. Table 5 summarizes the basic parameters that should be met for motor selection, which are as follows. The rotation angle of the motor at the hip joint should be larger than −12.232° to 24.387°, the motor speed should be faster than 150.216°/s, and the output torque should be greater than 0.703 Nm/kg; the rotation angle of the motor at the knee joint should be larger than 1.129°–65.433°, and the motor speed should be higher than 342.627°/s, and the output torque should be greater than 0.674 Nm/kg; the rotation angle range of the motor at the ankle joint should be larger than −13.556° to 19.022°, the motor speed should be faster than 310.042°/s, and the output torque should be greater than 1.751 Nm/kg.

Table 5.

Motor selection reference parameters.

Motor location	Scope of activities (°)	Angular velocity (°/s)	Moment (Nm/kg)
Hip	−12.232 to 24.387	150.216	0.703
Knee	1.129–65.433	342.627	0.674
Ankle	−13.556 to 19.022	310.042	1.751

Mechanical design of HLLE

Figure 4 shows the actuator and energy supply equipment used in the experiment. Figure 4(a) displays the servo, which provided the torque output to the HLLE’s joints; Figure 4(b) presents the motorized actuator mounted at the thigh linkage and shank linkage of the HLLE. The motorized actuator was used to adjust the length of the thigh linkage and shank linkage of the HLLE precisely. Finally, Figure 4(c) shows a lithium battery, which denoted the energy supply device of the HLLE. The technical parameters of the servo and electric drive pusher are given in Tables 6 and 7, respectively.

Figure 4.

The actuator and energy supply equipment: (a) servo, (b) motorized actuator, and (c) lithium battery.

Table 6.

Technical parameters of the ASMG-MT magnetic encoded servo.

Parameter	Value
Rated voltage	12–24 V/DC
Limed-Cur	10 A
Weight	550 g
End range	360°
Rated speed	500 r/s
Torque	50 Nm

Table 7.

Technical parameters of the electric drive pusher.

Parameter	Voltage(V)	Current(A)	Stroke(mm)	Maximumthrust (kg)
Value	24	2	100	100

The HLLE system consisted of six servos, four actuators, and a low-power control system. Two lithium batteries with a capacity of 30 AH and an output voltage of 24 V were used to supply energy. According to the device’s power, the endurance time of the lithium battery was calculated as follows:

$$\begin{array}{c}\multicolumn{1}{c}{\mathrm{\Delta }t=\frac{U_{\mathrm{Li}}{C}_{\mathrm{Li}}}{P_m+P_{\mathrm{push}}}\times k_{\mathrm{Li}}=\frac{2\times 24V\times 30\mathrm{AH}}{240w\times 6+48w\times 4}}\\ \multicolumn{1}{c}{\times 0.9=47.647\min }\end{array}$$

(1)

where $\mathrm{\Delta }\mathrm{t}$ is the range time; ${\mathrm{U}}_{\mathrm{Li}}$ is the voltage of the Li-ion battery; ${\mathrm{C}}_{\mathrm{Li}}$ is the capacity of the Li-ion battery; ${\mathrm{P}}_{\mathrm{m}}$ is the total power of the servo; ${\mathrm{P}}_{\mathrm{push}}$ is the total power of the pusher; ${\mathrm{k}}_{\mathrm{Li}}$ is the discharge factor of the Li-ion battery. The endurance time of the lithium battery met the requirements of the experiment.

The thigh, shank, foot, and waist linkages of the HLLE were provided with holes for the nylon straps to pass through, as shown in the complete assembly diagram of the HLLE presented in Figure 5. The HLLE and the human body were held in place by the nylon straps.

Figure 5.

Complete assembly drawing of the HLLE.

The mechanical design of the HLLE’s joints is shown in Figure 6. The HLLE’s hip, knee, and ankle joints were designed with limiting slots and blocks to prevent uncontrolled over-rotation of the rudder. The structural design of the HLLE at the hip joint retained three degrees of freedom to improve the comfort of the exoskeleton. The 3D model of the exoskeleton hip joint is presented in Figure 6(a). The mechanical joint’s movement was performed around the horizontal plane axis (i.e. axis 1), coronal plane axis (i.e. axis 2), and the sagittal plane axis (i.e. axis 3). An exploded view of the hip joint in the sagittal plane is displayed in Figure 6(b). The installation of a rudder at axis 3 could assist the wearer’s movement in the sagittal plane. Figure 6(c) shows the knee structure retaining only the degrees of freedom in the sagittal plane and adding servos in the sagittal plane. Figure 6(d) illustrates the ankle joint consisting of a rudder, a limit block, a shank linkage, and a foot linkage. The ankle retained only sagittal freedom. Further, Figure 6(e) shows the mechanics of the metatarsophalangeal joint of the foot. A single-degree-of-freedom kinematic vice was added to the metatarsophalangeal joint, and it flexed and extended during walking. In addition, the toe and heel were designed to arc to distribute impact forces; the midsole was hollowed out to reduce the weight.

Figure 6.

Mechanical design of the HLLE’s joints: (a) hip, (b) articular structure of the hip joint in the sagittal, (c) knee, (d) ankle, and (e) metatarsophalangeal joint.

An exploded view of the HLLE parts’ connections is presented in Figure 7; Figure 7(a) shows the waist connections of the HLLE. The right and left hip joints of the HLLE were connected by a lumbar linkage, which was secured with half-tooth bolts. Unthreaded holes in the lumbar linkage retained horizontal plane freedom, and threaded holes in the hip joint components secured the half-tooth bolts. The lumbar linkage had two rectangular holes for threading nylon straps to secure it to the lumbar region.

Figure 7.

Mechanical design of the connecting rods at each joint of HLLE: (a)waist connection,(b)connecting rod at right thigh,(c)connecting rod at right calf, (d)the connecting rod between the foot and ankle, and (e)power supply at the calf.

The lower limb exoskeleton of the HLLE had a symmetrical left–right structure, and the right side was used as an example in this study. Figure 7(b) and (c) show the connection of the right-side thigh and shank components of the HLLE. A motorized actuator was embedded between the hip and knee joints, and between the knee and ankle joints. The fixation was the same at both locations. The top of the actuator telescopic rod was bolted to the leg attachment bar via the actuator shaft retainer. The bottom of the putter was secured to the drive mounting plate with a putter tail retainer, and it was also bolted. The thigh and shank connecting rods had two rectangular holes for threading nylon straps to secure them to the legs.

The design of the foot member to the ankle joint connection of the HLLE is presented in Figure 7(d). An L-shaped linkage was used and bolted. The vertical distance between the center of the motor shaft hole on the ankle linkage and the foot member was the same as the distance from the center of the subject’s ankle joint to the foot bottom to ensure that the center of rotation of the actuator was aligned with the human ankle joint’s center.

The two lithium batteries used for the power supply device, which were fixed to the outside of the left and right shanks of the HLLE, are presented in Figure 7(e). In addition, four brackets were designed to clamp the power supply to the actuators at the HLLE’s calves. The bolt through the ankle drive mounting plate withstood the gravity of the power supply and prevented slipping. The other two bolts were located at the front and back of the power supply to prevent sliding back and forth.

Kinematic and kinetic analyses of HLLE

The ADAMS simulation software established the system’s dynamical equations using the Lagrange equation method. The sparse matrix technique and rigid integration algorithm were selected as computational means. This method improves computational efficiency to a great extent.

Motion equations

Under complete constraints, the number of constraint equations for the kinematic vice was assumed to be nh. The set of kinematic constraint equations was expressed using the system’s generalized coordinate vector as:

$${\mathrm{\Phi }}^K\left(q\right)={[{\mathrm{\Phi }}_1^K\left(q\right),{\mathrm{\Phi }}_2^K,\dots ,{\mathrm{\Phi }}_{\mathrm{nh}}^K(q)]}^T=0$$

(2)

The actual simulation required the system to have deterministic motion, so the number of degrees of freedom was zero. The same number of drive constraint equations was imposed based on the degrees of freedom the system, which can be expressed as:

$${\mathrm{\Phi }}^D(q,t)=0$$

(3)

Combining (2) and (3) yielded the full constraints of the entire system:

$$\mathrm{\Phi }(q,t)=\left[\begin{array}{c}{\mathrm{\Phi }}^K(q,t)\hfill \\ \multicolumn{1}{c}{{\mathrm{\Phi }}^D(q,t)}\end{array}\right]=0$$

(4)

Assuming that there were nc equations in (4), the set of these equations constituted the position equation of the system, and its derivation yielded the velocity constraint equation:

$${\mathrm{\Phi }}^{\prime }(q,q,t)={\mathrm{\Phi }}_q(q,t)q+{\mathrm{\Phi }}_t(q,t)=0$$

(5)

Let $\mathrm{\upsilon }=-{\mathrm{\Phi }}_{\mathrm{t}}(\mathrm{q},\mathrm{t})$ ; then, the velocity constraint equation was simply expressed as follows:

$${\mathrm{\Phi }}^{\prime }(q,q,t)={\mathrm{\Phi }}_q(q,t)q-\upsilon =0$$

(6)

The acceleration equation was obtained by taking the derivative of (5):

$$\begin{array}{c}\multicolumn{1}{c}{{\mathrm{\Phi }}^{″}(q,q,q,t)={\mathrm{\Phi }}_q(q,t)q+({\mathrm{\Phi }}_t(q,t)q{)}_{q}q+2{\mathrm{\Phi }}_{\mathrm{qt}}(q,t)q}\\ \multicolumn{1}{c}{+{\mathrm{\Phi }}_{\mathrm{tt}}(q,t)=0}\end{array}$$

(7)

Next, let $\mathrm{\eta }=-{\left({\mathrm{\Phi }}_{\mathrm{t}}(\mathrm{q},\mathrm{t})\mathrm{q}\right)}_{\mathrm{q}}\mathrm{q}-2{\mathrm{\Phi }}_{\mathrm{qt}}(\mathrm{q},\mathrm{t})\mathrm{q}-{\mathrm{\Phi }}_{\mathrm{tt}}(\mathrm{q},\mathrm{t})$ ; then, the acceleration equation was defined as:

$${\mathrm{\Phi }}^{″}(q,q,q,t)={\mathrm{\Phi }}_q(q,t)q-\eta (q,q,t)=0,$$

(8)

where ${\mathrm{\Phi }}_{\mathrm{q}}$ is a Jacobi matrix; when its dimension was m and the dimension of q was n, ${\mathrm{\Phi }}_{\mathrm{q}}$ ’s denoted matrices of dimension m × n defined by:

$$({\mathrm{\Phi }}_q{)}_{(i,j)}=\frac{\partial {\mathrm{\Phi }}_i}{\partial {\mathrm{\Phi }}_j}$$

(9)

In (9), ${\mathrm{\Phi }}_{\mathrm{q}}$ contains nh kinematic constraints, (nc – nh) driving constraints, and nc generalized coordinates.

The position, velocity, acceleration, and constraint reaction forces were studied when the system had zero degrees of freedom. Therefore, only the constraint equations of the system needed to be solved:

$$\mathrm{\Phi }(q,t_n)=0$$

(10)

The position of moment $t_n$ in motion was obtained using the Newton–Raphson iterative method as:

$${\mathrm{\Phi }}_{\mathrm{qj}}\mathrm{\Delta }{q}_j+\mathrm{\Phi }(q_j,t_n)=0,$$

(11)

where $\mathrm{\Delta }{\mathrm{q}}_{\mathrm{j}}={\mathrm{q}}_{\mathrm{j}+1}-{\mathrm{q}}_{\mathrm{j}}$ for the jth iteration.

The velocity and acceleration at any moment during the motion could be solved by the CALAHAN and HARWELL method.

Kinetic equation

Assume that the generalized coordinates of a rigid body in the system are $\mathrm{q}=[\mathrm{x},\mathrm{y},\mathrm{z},\mathrm{\psi },\mathrm{\theta },\mathrm{\phi }{]}^{\mathrm{T}}$ , so that $\mathrm{R}=[\mathrm{x},\mathrm{y},\mathrm{z}{]}^{\mathrm{T}}$ , $\mathrm{\gamma }=[\mathrm{\psi },\mathrm{\theta },\mathrm{\phi }{]}^{\mathrm{T}}$ , $\mathrm{q}=[{\mathrm{R}}^{\mathrm{T}},{\mathrm{\gamma }}^{\mathrm{T}}]$ . The coordinate transformation matrix of this rigid body with respect to the ground coordinate system was defined by:

$$A^{\mathrm{gi}}=\left[\begin{array}{ccc}\cos \psi \cos \varphi -\sin \psi \cos \theta \sin \varphi \hfill & -\cos \psi \sin \varphi -\sin \psi \cos \theta \cos \varphi \hfill & \sin \psi \sin \theta \hfill \\ \multicolumn{1}{c}{\sin \psi \cos \varphi +\cos \psi \cos \theta \sin \varphi }& -\sin \psi \sin \varphi +\cos \psi \cos \theta \cos \varphi \hfill & -\cos \psi \sin \theta \hfill \\ \multicolumn{1}{c}{\sin \theta \sin \varphi }& \sin \theta \sin \phi \hfill & \cos \theta \hfill \end{array}\right]$$

(12)

Next, an additional Eulerian rotation axis coordinate system was defined. The unit vector of its coordinate axis was the rotation axis of the Euler angles of the rigid body mentioned above. Its coordinate transformation matrix to the center-of-mass coordinate system of the rigid body was defined as:

$$\left[B\right]=\left[\begin{array}{ccc}\sin \theta \sin \varphi \hfill & 0\hfill & \cos \theta \hfill \\ \multicolumn{1}{c}{\sin \theta \cos \varphi }& 0\hfill & -\sin \theta \hfill \\ \multicolumn{1}{c}{\cos \theta }& 1\hfill & 0\hfill \end{array}\right]$$

(13)

The angular velocity of a rigid body was expressed by:

$$\omega =B{\gamma }^{\prime }$$

(14)

Variable ${\omega }_{\mathrm{e}}$ was introduced into the ADAMS as a component of the angular velocity in the Eulerian rotational axis coordinate system, and it was defined by:

$${\omega }_e={\gamma }^{\prime }$$

(15)

Because of the implementation of the constraint equations, the ADAMS was obtained using the energy form of the Lagrangian Type I equations with Lagrange multipliers as:

$$\frac{d}{\mathrm{dt}}\left(\frac{\partial E}{\partial q_j}\right)-\frac{\partial E}{\partial q_j}=Q_j+\sum _{i=1}^n{\lambda }_i\frac{\partial \mathrm{\Phi }}{\partial q_j},$$

(16)

where E is the kinetic energy of the system in generalized coordinates; ${\mathrm{q}}_{\mathrm{j}}$ is the generalized coordinate; ${\mathrm{Q}}_{\mathrm{j}}$ is the generalized force in the direction of ${\mathrm{q}}_{\mathrm{j}}$ ; the last term on the right-hand side of the equation denotes the constrained reaction force in the direction of ${\mathrm{q}}_{\mathrm{j}}$ .

The constraint reaction force was simplified to:

$$C_j=\sum _{i=1}^n{\lambda }_i\frac{\partial \mathrm{\Phi }}{\partial q_j}$$

(17)

The ADAMS introduced generalized momentum as:

$$P_j=\frac{\partial E}{\partial {q^{\prime }}_j}$$

(18)

Next, substituting ${\mathrm{C}}_{\mathrm{j}}$ and ${\mathrm{P}}_{\mathrm{j}}$ into (16) yielded:

$$P_j-\frac{\partial E}{\partial q_j}=Q_j-C_j$$

(19)

and T was expressed by:

$$T=\frac{1}{2}{R}^T\mathrm{MR}+\frac{1}{2}{\gamma }^{\prime }{B}^T\mathrm{JB}{\gamma }^{\prime },$$

(20)

where J is the inertia matrix of the rigid body in the center-of-mass coordinate system, and M is the mass matrix of the rigid body.

According to (19), the directions of movement and rotation were respectively obtained as:

$$P_R-\frac{\partial E}{\partial q_R}=Q_R-C_R$$

(21)

$$P_{\gamma }-\frac{\partial E}{\partial q_{\gamma }}=Q_{\gamma }-C_{\gamma }$$

(22)

Since ${\mathrm{P}}_{\mathrm{R}}=\frac{\mathrm{d}}{\mathrm{dt}}\left(\frac{\partial \mathrm{T}}{\partial {\mathrm{q}}_{\mathrm{R}}}\right)=\frac{\mathrm{d}}{\mathrm{dt}}\left(\mathrm{MR}\right)=\mathrm{MV},\frac{\partial \mathrm{T}}{\partial {\mathrm{q}}_{\mathrm{R}}}=0$ , (21) was simplified as:

$$\mathrm{MV}=Q_R-C_R$$

(23)

Based on the above derivation, each component in the model had 15 variables and 15 equations. The ADAMS automatically defined the dynamics equations of the system as:

$$\{\begin{array}{c}P-\frac{\partial E}{\partial q}+{\mathrm{\Phi }}_q^{T\lambda }+H^{T}F=0\hfill \\ \multicolumn{1}{c}{P=\frac{\partial E}{\partial q}}\\ \multicolumn{1}{c}{u=q}\\ \multicolumn{1}{c}{\mathrm{\Phi }(q,t)=0}\\ \multicolumn{1}{c}{F=f(u,q,t)}\end{array}$$

(24)

where P is the generalized momentum of the system, and H is the coordinate change matrix of the external force.

The ADAMS adopted the DAE equation direct solution and ODE equation solution to solve the system’s dynamics equations. The direct solution of the DAE equations was obtained by applying the first-order backward difference formula so that the system of equations in (24) could be derived with respect to (u, q, λ), which yielded the Jacobian matrix, which was solved using the Newton–Rapson formula. The solving method of the ODE equation used constraint equations to decompose the generalized coordinates of the DAE equation into independent and non-independent coordinates so that it reduced to the ODE equation solving.

Kinematics and dynamics simulation of HLLE

Based on subject dimensions, a simple 3D model of the human body was created. The HLLE model and the human body model were coupled in the ADAMS software. The coupled human model standing on a simulated walkway is presented in Figure 8.

Figure 8.

The coupled model of the HLLE and human body in the ADAMS environment.

Since only the human–machine coupled model was studied in the sagittal plane when walking, rotating subs were added to the hip, knee, and ankle joints, and fixed subs were added to the rest of the connections. In addition, parallel subs associated with the ground were added to the left and right feet and waist to ensure stabilized walking of the human–machine coupled model. The CUBSPL function in the ADAMS drove the rotating sub. The results of the HGD analysis showed that the joint torque and collision force were proportional to the velocity. The data on the hip and knee joint angles during walking at the speed of ${\mathrm{v}}_3=1.147\mathrm{m}/\mathrm{s}$ were imported into the ADAMS to generate the corresponding spline curve. The spline curve was converted into the CUBSPL function entry parameters. The materials and parameters of the components of the HLLE are shown in Table 8.

Table 8.

Properties of materials used in the HLLE.

Stuff	6061-t6	Alloy steel	Carbon steel	Epoxy resin	Aluminum
Density ( $\mathrm{kg}/{\mathrm{m}}^3$ )	2713	7850	7850	1857	2770
Young’s modulus ( $\mathrm{GPa}$ )	69.04	212.5	212.4	26.4	71
Poisson’s ratio	0.33	0.29	0.29	0.15	0.33
Bulk modulus ( $\mathrm{GPa}$ )	67.69	168.65	168.57	12.73	69.61
Shear modulus ( $\mathrm{GPa}$ )	25.96	82.36	82.33	14.36	26.69
Yield strength ( $\mathrm{MPa}$ )	259.2	652.2	293.5	440.1	280
Position	Connecting rodsand retainers	Shafts and gearsfor servos	Bolts	Power supplyhousing	Servo housingand pushrods

Simulation data analysis

The displacements of the ankle joint in the direction perpendicular to the walkway (the Z-axis) and in the horizontal plane (the Y-axis) were determined. In Figure 9, RACZ and RACY denote the displacement curves of the right ankle center in the directions of the Z and Y axes, respectively; LACZ and LACY are the displacement curves of the left ankle center in the Z-axis and Y-axis directions, respectively. The displacement range of the ankle joint center on the Z-axis was within 375 mm, and its displacement curve was periodic with the period of T = 1.16 s. The ankle joint made up and down periodic motions during walking. The general trend of the displacement curve of the ankle center on the Y-axis was incremental because the whole manikin model was moving forward. The RACY and LACY curves at a larger ascending curvature corresponded to an ankle that was in the swing phase. Subsequent slowing of the curvature of the curve indicated that the ankle shifted from the swing phase to the stance phase. A slight downward trend in the curve occurred when the ankle shifted from the stance phase to the backward swing phase.

Figure 9.

Displacement of the ankle center in the vertical and horizontal planes.

Figure 10 shows the displacement curves of the ankle center over time; Figure 10(a) and (b) show the drive center displacement data ( ${\mathrm{P}}_{\mathrm{SYLA}}$ , ${\mathrm{P}}_{\mathrm{SYRA}}$ ) at the exoskeleton ankle joint versus the human ankle center displacement data ( ${\mathrm{P}}_{\mathrm{MYLA}}$ , ${\mathrm{P}}_{\mathrm{MYRA}}$ ) on the Y-axis with respect to time t in both the simulation and experimental environments. As shown in Figure 10(a), at t = 0.33 s, ${\mathrm{P}}_{\mathrm{SYLA}}={\mathrm{P}}_{\mathrm{MYLA}}$ , which indicated that the simulated position of the left ankle center coincided with the experimental position. The difference between the maximum magnitude of the simulation curve, ${\mathrm{P}}_{\mathrm{SYLAMax}}$ , and the maximum magnitude of the kinetic capture curve, ${\mathrm{P}}_{\mathrm{MYLAMax}}$ , was 29.7%. Further, Figure 10(b) shows that at t = 0.29 s, ${\mathrm{P}}_{\mathrm{SYRA}}={\mathrm{P}}_{\mathrm{MYRA}}$ , which indicated that the maximum magnitude of the simulation curve, ${\mathrm{P}}_{\mathrm{SYRAMax}}$ , differed from the maximum magnitude of the kinetochore curve, ${\mathrm{P}}_{\mathrm{MYRAMax}}$ , by 34.8%. In addition, displacements ${\mathrm{P}}_{\mathrm{SZLA}}$ and ${\mathrm{P}}_{\mathrm{SZRA}}$ of the left and right ankle joint centers in the simulation environment and displacements ${\mathrm{P}}_{\mathrm{MZLA}}$ and ${\mathrm{P}}_{\mathrm{MZRA}}$ in the experimental environment on the Z-axis are presented as a function of time t in Figure 10(c) and (d), respectively. As presented in Figure 10(c), the maximum moment of difference in the amplitude between the simulation and trapping curves was at t = 1.57 s. The maximum magnitude of the simulation curve, ${\mathrm{P}}_{\mathrm{SZLAMax}}$ , was 6.1% larger than the maximum magnitude of the trapping curve, ${\mathrm{P}}_{\mathrm{MZLAMax}}$ . Figure 10(d) shows that the maximum difference in the amplitude between the simulation and trapping curves was at t = 0.97 s. The maximum magnitude of the simulation curve, ${\mathrm{P}}_{\mathrm{SZRAMax}}$ , was 13.9% larger than the maximum magnitude of the trapping curve, ${\mathrm{P}}_{\mathrm{MZRAMax}}$ . The ankle center of the HLLE’s model on the Z-axis fitted better with the motion capture data on the Z-axis. The reason for the large difference in the Y-axis was that the origin of the global coordinate system of the motion capture system differed from the origin of the global coordinate system of the simulation environment. In general, the trends of the kinematic and simulation curves were almost the same. Therefore, the structural design of the HLLE could meet the requirements in terms of kinematics.

Figure 10.

Displacement curves of the ankle center: (a) left ankle center on the Y-axis, (b) right ankle center on the Y-axis, (c) left ankle center on the Z-axis, and (d) the right ankle joint on the Z-axis.

The variation rules of the left and right hip joint moments ${\mathrm{M}}_{\mathrm{LH}}$ and ${\mathrm{M}}_{\mathrm{RH}}$ with the gait time t of the human–machine coupling model are presented in Figure 11. The right hip joint moment reached its maximum peak value ${\mathrm{M}}_{\mathrm{RHPe}}=371.368\mathrm{Nm}$ at t = 1.73, and the maximum range of variation of the right hip joint moment $\mathrm{\Delta }{\mathrm{M}}_{\mathrm{RHMax}}=1915.070\mathrm{Nm}$ was during the interval t = 0–2.13 s. The absolute value of the mean value of the moment $\left|{\mathrm{M}}_{\mathrm{\mu }\mathrm{RH}}\right|$ was 4.1% of $\mathrm{\Delta }{\mathrm{M}}_{\mathrm{RHMax}}$ ; this was caused by the impact force from the ground. At t = 1.14 s, the left hip reached a maximum peak ${\mathrm{M}}_{\mathrm{LHPe}}$ , which was 96.0% of ${\mathrm{M}}_{\mathrm{RHPe}}$ . The maximum variation of moment $\mathrm{\Delta }{\mathrm{M}}_{\mathrm{LHMax}}$ was 43.5% of $\mathrm{\Delta }{\mathrm{M}}_{\mathrm{RHMax}}$ , and it occurred from t = 0 to t = 2.13 s. The absolute value of the average moment value $|{\mathrm{M}}_{\mathrm{\mu }\mathrm{LH}}|$ was 25.7% of $\left|{\mathrm{M}}_{\mu \mathrm{RH}}\right|$ .

Figure 11.

Moment values of the hip joint of the HLLE in the simulations.

Figure 12 demonstrates the variation patterns of the left and right knee moments ${\mathrm{M}}_{\mathrm{LK}}$ and ${\mathrm{M}}_{\mathrm{RK}}$ of the human–machine coupled model with gait time t. The right knee joint moment reached its maximum peak value ${\mathrm{M}}_{\mathrm{RKPe}}=229.418\mathrm{Nm}$ at t = 1.73 s. The maximum range of variation of the right knee joint moment of $\mathrm{\Delta }{\mathrm{M}}_{\mathrm{RKMax}}=987.394\mathrm{Nm}$ was observed from t = 0 to t = 2.13 s. The absolute value of the mean value of the moment $\left|{\mathrm{M}}_{\mathrm{\mu }\mathrm{RK}}\right|$ was 3.0% of $\mathrm{\Delta }{\mathrm{M}}_{\mathrm{RKMax}}$ . This was because the right knee joint aimed to overcome the impact force from the ground. At t = 1.14 s, the left knee reached a maximum peak ${\mathrm{M}}_{\mathrm{LKPe}}$ of 95.2% of ${\mathrm{M}}_{\mathrm{RKPe}}$ . The maximum variation range of the moment, $\mathrm{\Delta }{\mathrm{M}}_{\mathrm{LKMax}}$ , was 46.1% of $\mathrm{\Delta }{\mathrm{M}}_{\mathrm{RKMax}}$ , and it occurred from $\mathrm{t}=0$ to $\mathrm{t}=2.13\mathrm{s}$ . The absolute value of the average torque value $\left|{\mathrm{M}}_{\mathrm{\mu }\mathrm{LK}}\right|$ was 8.4% of $\left|{\mathrm{M}}_{\mathrm{\mu }\mathrm{RK}}\right|$ .

Figure 12.

Moment values of the knee joint of the HLLE in the simulation.

The analysis of the moment values of the hip and knee joints of the human–machine coupling model showed that the right hip joint was most affected by the impact force from the ground. The absolute value of the mean moment value at the right hip’s drive center was greater than that of the left hip. For human gait parameters, the mean value of moments was −3.852 Nm/kg for the left hip joint and −4.227 Nm/kg for the right hip joint. The absolute value of the mean moment of the right hip was greater than that of the left hip. In addition, the leg force habits demonstrated in the ADAMS simulations were consistent with those captured in the experiments. Additionally, except for the right hip joint, the mean value of the moments was greater than the holding torque of the selected rudder. The average value of the moments of the remaining joints was less than the holding torque of the servos. Further, it was verified that the selected servo had a booster effect. The changing trends of the collision forces ${\mathrm{F}}_{\mathrm{LF}}$ and ${\mathrm{F}}_{\mathrm{RF}}$ with time t for the left and right foot members of the 3D model of the exoskeleton are presented in Figure 13. The collision force applied to the right ankle joint reached a maximum collision force ${\mathrm{F}}_{\mathrm{RFMax}}=2758.233\mathrm{N}$ at t = 1.36 s. This was due to the first contact of the right foot member with the ground. In the time interval of $\mathrm{t}=0.75\mathrm{s}-1.33\mathrm{s}$ , the right leg was in the swing phase, and the foot member had no contact with the ground, so ${\mathrm{F}}_{\mathrm{RF}}=0$ . The left foot member produced the maximum collision force ${\mathrm{F}}_{\mathrm{LFMax}}$ at t = 0.75 s, which was 85.2% of ${\mathrm{F}}_{\mathrm{RFMax}}$ . The collision force on the left foot member was less than that on the right foot member.

Figure 13.

Simulation results of the collision force between the sole of the HLLE’s foot and the ground.

Finite element analysis of HLLE

In this study, the maximum factor of safety was used to determine whether the stresses to which the HLLE was subjected could satisfy the strength requirements. The maximum stress denoted the maximum stress that the study object could withstand within the allowable stress range of the material. According to the static analysis, the allowable stress of the study object was defined by:

$$\left[\sigma \right]=\frac{{\sigma }_b}{n}$$

(25)

where ${\mathrm{\sigma }}_{\mathrm{b}}$ is the ultimate strength, and n is the safety factor.

Due to its structural complexity, the HLLE was reduced to a mathematical model, and the system equations are as follows:

$$\left[M\right]\left\{\stackrel{··}{x}\right\}+\left[K\right]\left\{x\right\}=\{F(t)\}$$

(26)

The position vector {x} in the matrix model of the HLLE was defined as [Δ]{u}, where [Δ] denoted the system’s modal matrix, and the external force vector was {F(t)} = 0. Then (26) could be modified to the following form:

$$\left[I\right]\left\{\stackrel{··}{x}\right\}+\left[A\right]\left\{x\right\}=\{0\},$$

(27)

Where

$${\left[\mathrm{\Delta }\right]}^T\left[M\right]\left[\mathrm{\Delta }\right]=\left[I\right]=\left[\begin{array}{cccc}1\hfill & 0\hfill & \dots \hfill & 0\hfill \\ \multicolumn{1}{c}{0}& 1\hfill & \dots \hfill & ⋮\hfill \\ \multicolumn{1}{c}{⋮}& 0\hfill & \ddots \hfill & 0\hfill \\ \multicolumn{1}{c}{0}& 0\hfill & 0\hfill & 1\hfill \end{array}\right]$$

(28)

$${\left[\mathrm{\Delta }\right]}^T\left[K\right]\left[\mathrm{\Delta }\right]=\left[A\right]=\left[\begin{array}{cc}\begin{array}{cc}\overline{{\omega }_1^2}\hfill & 0\hfill \end{array}\hfill & \begin{array}{cc}\dots \hfill & 0\hfill \end{array}\hfill \\ \multicolumn{1}{c}{\begin{array}{cc}\begin{array}{c}0\hfill \\ \multicolumn{1}{c}{\begin{array}{c}⋮\hfill \\ \multicolumn{1}{c}{0}\end{array}}\end{array}\hfill & \begin{array}{c}\overline{{\omega }_2^2}\hfill \\ \multicolumn{1}{c}{\begin{array}{c}0\hfill \\ \multicolumn{1}{c}{\cdots }\end{array}}\end{array}\hfill \end{array}}& \begin{array}{c}\begin{array}{cc}\cdots \hfill & ⋮\hfill \end{array}\hfill \\ \multicolumn{1}{c}{\begin{array}{cc}\begin{array}{c}\ddots \hfill \\ \multicolumn{1}{c}{0}\end{array}\hfill & \begin{array}{c}0\hfill \\ \multicolumn{1}{c}{\overline{{\omega }_n^2}}\end{array}\hfill \end{array}}\end{array}\hfill \end{array}\right]$$

(29)

The intrinsic frequency of the detuned system was defined by:

$$\overline{{\omega }_n}=\frac{{\omega }_n}{\sqrt{\frac{\mathrm{EI}}{\rho A{L}^4}}},n=1,2,3$$

(30)

Before performing the finite element analysis on the HLLE, its 3D model was simplified, but this did not affect the analysis results. The 3D model of the HLLE after removing the chamfers and simplifying the rudder and actuator is shown in Figure 14.

Figure 14.

Simplified 3D HLLE model.

In the finite element analysis, the HLLE’s standing, swing, single limb support, and double limb support phases were analyzed. Figure 15 shows the meshing of the simplified 3D HLLE model, and the average values of the mesh skewness in the four phases were within the range of 0–0.5, as shown in Table 9. This indicated that the meshing could meet the requirements.

Figure 15.

Meshing of the simplified 3D HLLE model.

Table 9.

Mesh skewness values of the HLLE model in the four phases.

Attitude	Standing	Swing	Single limb support	Double limb support
Skewness average	0.356	0.412	0.427	0.349

The total load applied to the HLLE model was 1000 N. The constraints and loads of the HLLE in the four phases were set according to the HGD analysis, as shown in Table 10.

Table 10.

Loads applied to the HLLE model in different phases.

Attitude	Lefthip ( $\mathrm{N}$ )	Righthip ( $\mathrm{N}$ )	Orientation
Standing	500	500	Vertical down
Swing	400	600	Vertical down
Single limb support	200	800	Vertical down
Double limb support	300	1000	Vertical down

Table 11 lists the maximum stresses and their locations in these phases. The strength and stiffness requirements of the HLLE were considered from the point of view of maximum stresses.

Table 11.

Maximum stresses at different attitudes and locations of the occurring stresses.

Attitude	Maximum stress value ( $\mathrm{MPa}$ )	Maximum stress location
Standing	37.232	At the bolt on the bottom of the pushrod at the left shank
Swing	59.976	Linkage that connects the right hip joint to the right thigh thrusters
Single limb support	12.483	Right hip drive
Double limb support	134.22	Right shank at the bottom retainer of the putter

The modal analysis extracted the first six orders of modes. The intrinsic frequency, maximum deformation, and location of occurrence of the HLLE in the standing and double limb support phases are presented in Table 12, respectively. The first six orders of modes of the HLLE model in the double limb support phase are presented in Figure 16.

Table 12.

Intrinsic frequency, maximum deformation, and location of occurrence of the 3D HLLE model in the double limb support phase.

Modal order	Fundamentalfrequency ( $\mathrm{Hz}$ )	Maximumdeformation( $\mathrm{mm}$ )	Characteristics of the vibration pattern
1	23.086	12.067	Swing from side to side at the waist linkage
2	29.994	19.209	Swing up and down at the linkage that connects the right hip to the psoas
3	38.443	11.223	Swing from side to side at the right hip
4	40.827	16.333	Twisting in a horizontal plane at the left hip joint
5	64.696	14.035	Swing from side to side at the waist linkage
6	76.74	24.671	Swing up and down at the waist linkage

Figure 16.

The first sixth-order modal vibrations of the 3D HLLE model in the double-limb support phase: (a) first, (b) second, (c) third, (d) fourth, (e) fifth, and (f) sixth.

The analysis results could be summarized as follows:

1. There was no abrupt change in the vibration pattern of the HLLE model between the two attitude values, which indicated that the bending stiffness of its components was reasonable.

2. According to the HGD, the maximum angular velocity of the knee joint reached 57.105 RPM, and at this point, the maximum operating frequency of the motor was 0.952 Hz. The first-order intrinsic frequencies of the HLLE model in the standing and double limb support phases were 18.239 and 23.086 Hz, respectively, and they were both larger than the maximum frequency of the motor; therefore, there was no resonance in these two phases.

3. The human body normally walks between 1.209 and 2.048 Hz. However, the results indicated that the HLLE model’s first-order frequency was above this range both in the standing and double limb support phases. Therefore, there was no resonance during walking with the HLLE.

Control system design and experimentation

The main controller of the HLLE’s control system was an FPGA, which used the pressure value from the pressure sensor as input and output the angle value of the servo. The block diagram of the control system’s hardware is presented in Figure 17, where the arrows indicate the direction of signal transmission. The pressure sensor sensed the pressure between the human body and the HLLE, the conversion module converted this pressure into a digital signal, which was then processed by the FPGA to obtain the pressure value. The FPGA controlled the rotation of the servo by sending control signals to the servo driver board, which then controlled the rotation of the servo. The rotation angle of the servo was converted into a digital signal and transmitted to the FPGA for processing to obtain the corresponding angle value. The pressure and servo angle values output by the FPGA were used to debug the HLLE’s control system.

Figure 17.

Block diagram of the control system’s hardware.

The main controller of the control system used XLINX’s XC7A35T chip, which received digital signals from the sensors and output the PWM waves to control the motor. The sensor module was used to capture the man-machine pressure. The AD conversion module converted the analog signals from the pressure sensor module to digital signals and processed the feedback angle data obtained from the servo. The servo drive module received the PWM signals from the controller and used then to control servo rotation and provide feedback on the servo rotation angle. The control method for the exoskeleton was the state transfer method (STM). The STM (Figure 19) triggered state transitions based on pressure values, with different numbers indicating different transition conditions. The STM divided walking into four phases: standing, lifting the leg forward, stomping backward, and shifting the center of gravity. For instance, when the right thigh was lifted first, the walking sequence was: 1, 2, 3, 5, 6; when the left thigh was lifted first, the walking sequence was: 4, 5, 6, 2, 3. As shown in Figure 18, it is a schematic diagram of the vertical force component exerted on the pressure sensor on the human-machine contact surface when the subject wears the HLLE and walks. The pressure sensor was mounted between the nylon strap and the surface of the body, and a mass equivalent was used to indicate the pressure value. There was a pressure sensor at the front and rear of the thigh. f0 indicates the pressure value of the pressure sensor at the front of the thigh, while b0 indicates the pressure value of the pressure sensor at the rear of the thigh. There was also a pressure sensor at the front and rear of the shank. f1 indicates the pressure value of the pressure sensor at the front of the shank, and b1 indicates the pressure value of the pressure sensor at the rear of the shank. There was also a pressure sensor at the instep and at the heel; f2 indicates the pressure value of the pressure sensor at the front of the instep, while b2 indicates the pressure value of the pressure sensor at the rear of the heel.

Figure 18.

Vertical force component of the pressure sensor on the human-machine interface.

Figure 19.

Kinematic state transfer process in the HLLE.

The force transmission mechanism and human-machine coordination process of HLLE in this paper include the influence of external load. Based on this situation, the motor torque expressions of the hip, knee, and ankle joints are derived. The HLLE in this paper provides active assistance through motors installed at the hip, knee, and ankle joints. The power output path is in the order of motor, reducer, HLLE connecting rod, wearable bandage, human joints plus external load. In this process, the external load is transmitted to the ground through the leg structure, and the motor needs to output additional torque to offset the gravity and inertia load caused by the increase in weight. In Figure 18, ${\theta }_1{\theta }_2{\theta }_3$ are the angles of the hip, knee, and ankle joints, $m_1{m}_2{m}_3$ are the masses of each link, $m_L$ is the mass of the external load, and ${\tau }_1{\tau }_2{\tau }_3$ are the torques output by the motors of the hip, knee, and ankle joints. Combining the Lagrangian method and considering the influence of mass $m_L$ and center of gravity height $h_L$ on dynamics, the equivalent gravity term of the load introduced at the hip joint is obtained:

$${\tau }_1=I_1{\stackrel{··}{\theta }}_1+m_{1}g\frac{l_1}{2}\cos \left({\theta }_1\right)+m_{L}g{h}_L\cos \left({\theta }_1\right)+f_{\mathrm{dyn}}^{(1)}$$

(31)

The knee and ankle joint dynamics remain as follows:

$${\tau }_2=I_2{\stackrel{··}{\theta }}_2+m_{2}g\frac{l_2}{2}\cos ({\theta }_1+{\theta }_2)+f_{\mathrm{dyn}}^{(2)}$$

(32)

$${\tau }_3=I_3{\stackrel{··}{\theta }}_3+m_{3}g\frac{l_3}{2}\cos ({\theta }_1+{\theta }_2+{\theta }_3)+f_{\mathrm{dyn}}^{(3)}$$

(33)

Where $I_1{I}_2{I}_3$ are the moments of inertia of each link, g is the acceleration of gravity, $l_1{l}_2{l}_3$ are the lengths of the thigh, calf, and foot, and $f_{\mathrm{dyn}}^{(i)}$ represents the dynamic term generated by the coupling between the links.

The state transfer conditions depended on the pressure transducer values, as shown in Table 13. The initial state of the HLLE was the standing state. In addition, after pressing the reset button, the control system would return the current HLLE’s state to its initial state.

Table 13.

Motion state transfer conditions.

Serial number ofthe conversion condition	Conversion conditions
1	$f0>600g$ ; $b1>600g$ , $f1>6\mathrm{kg}$ , $f1>600g$ ; $f2>600g$
2	$b0>6\mathrm{kg}$ ; $b1>6\mathrm{kg}$ ; b2>14 kg
3	$f0>600g$ ; $f1>600g$ , $b1>6\mathrm{kg}$ ; $b1>600g$ ; $b2>14\mathrm{kg}$
4	$f0>600g$ ; $f1>600g$ , $b1>6\mathrm{kg}$ ; $b1>600g$ ; $b2>600g$
5	$f0>6\mathrm{kg}$ ; $f1>6\mathrm{kg}$ ; $f2>14\mathrm{kg}$
6	$f0>600g$ ; $b1>600g$ , $f1>6\mathrm{kg}$ , $f1>600g$ ; $f2>600g$
7	Reset
8	Reset
9	Reset

The EMG signals collected from the subject while walking with the HLLE are presented in Figure 20. The EMG signals were used to verify the power-assisting effect of the HLLE. The EMG signal collector monitored muscle contraction using the electrode pads attached to the thigh and shank, as shown in Figure 20(a). The acquired EMG signals were transmitted to the PC via Bluetooth for analysis, and the result was obtained and displayed using the SerialPlot software. The more pronounced the muscle contraction was, the larger the amplitude of the EMG signal was. In the absence of muscle contraction, the amplitude was essentially unchanged. Figure 20(b) shows a subject walking while wearing an exoskeleton with a 20-kg load and an EMG signal collector.

Figure 20.

Illustration of the acquisition process of electromyographic signals while walking in an exoskeleton: (a) wearing the EMG signal collector and (b) exoskeleton-wearing experiment.

Experimental data analysis

The left and right limbs of the human body are symmetrical, and the HLLE designed in this paper also takes the symmetry of the human body into consideration. Therefore, the analysis of the experimental results takes the right thigh and calf as an example to avoid redundancy in the analysis process.

In the experiments, each EMG signal meter had two channels to capture signals from two muscles simultaneously. The EMG signals of the right thigh are presented in Figure 21. Figure 21(a) shows the EMG signals of the right thigh acquired while walking without the HLLE and with a weight of 20 kg. The amplitude at time t = 0.743 s reached the maximum of ${\mathrm{A}}_{\mathrm{RThMax}}=2,953$ . The maximum variation range of amplitude was $\mathrm{\Delta }{\mathrm{A}}_{\mathrm{RTh}}=2,141$ . Figure 21(b) shows the EMG signals of the right thigh acquired while wearing the HLLE and walking with the 20-kg weight. The largest magnitude ${\mathrm{A}}_{\mathrm{RTh}}^{\prime }$ occurred at time t = 0.757 s, and it was 57.9% of ${\mathrm{A}}_{\mathrm{RThMax}}$ . The maximum variation range of the magnitude $\mathrm{\Delta }{\mathrm{A}}_{\mathrm{RTh}}^{\prime }$ was 15.5% of $\mathrm{\Delta }{\mathrm{A}}_{\mathrm{RTh}}$ . The exoskeleton had a booster effect on the right thigh.

Figure 21.

EMG signals of the right thigh obtained without and with the HLLE: (a) without the HLLE and (b) with the HLLE.

Figure 22 shows the EMG signals of the right shank. Figure 22(a) shows the EMG signal amplitude A_RCa of the right shank as a function of time t when the subject was weight-bearing but not wearing the HLLE. The maximum magnitude of ${\mathrm{A}}_{\mathrm{RCaMax}}=2,697$ occurs at time t = 1.008 s. The maximum variation range of the magnitude was $\mathrm{\Delta }{\mathrm{A}}_{\mathrm{RCa}}=172$ . Figure 22(b) shows the EMG signal amplitude ${\mathrm{A}}_{\mathrm{RCa}}^{\prime }$ of the right shank as a function of time t when the subject was weight-bearing and walking with the HLLE. The maximum magnitude ${\mathrm{A}}_{\mathrm{RCaMax}}^{\prime }$ occurred at t = 1.598 s, and it was 74.6% of ${\mathrm{A}}_{\mathrm{RCaMax}}$ . The maximum variation range of magnitude ${\mathrm{\Delta }\mathrm{A}}_{\mathrm{RCa}}^{\prime }$ was 41.6% of $\mathrm{\Delta }{\mathrm{A}}_{\mathrm{RCa}}$ . Therefore, the right shank was subjected to the boosting effect of the HLLE.

Figure 22.

EMG signals of the right shank obtained without and with the HLLE: (a) without the HLLE and (b) with the HLLE.

Conclusion

A new method for a human lower limb exoskeleton device that combines kinematics, vibration, biomechanics, and a machine vision motion capture system was developed in this paper. This method can replicate the physiological structure of human lower limbs, accurately and automatically follow the user’s movements, and assist the human body in weight-bearing walking. The main findings of this study can be summarized as follows:

1. A visual environment for capturing human motion parameters is constructed. The camera is calibrated with a maximum error of 0.893 mm, which demonstrates that the accuracy of the motion capture system can be controlled at the sub-millimeter level. Based on the subjects’ static standing data, the right leg’s length is defined as a basic parameter for designing the exoskeleton. The lengths of the right thigh and shank are determined to be 415.166 and 434.279 mm, respectively. By analyzing the subjects’ HGD in the sagittal plane, the maximum mobility in the sagittal plane of the hip, knee, and ankle joints is calculated to be 36.619°, 64.304°, and 32.578°, respectively. The faster the walking speed is, the larger the angle of motion and joint angular velocity of a joint, the shorter the gait cycle, and the greater the required joint torque output will be. The maximum angular velocity and the output moment of the hip joint are determined to be 150.216°/s and 0.703 Nm/kg, respectively. Similarly, the maximum angular velocity and the output moment of the knee joint are calculated to be 342.627°/s and 0.674 Nm/kg, respectively. Finally, the maximum angular velocity and the output moment of the ankle joint are 310.042°/s and 1.751 Nm/kg, respectively.

2. The HLLE uses six ASMG-MT magnetically encoded servos and four motorized actuators with a stroke of 100 mm, and the power supply uses two lithium batteries. The power supply has a range of 47.647 min. The HLLE’s mechanical design has three degrees of freedom at the hip joints, and the knee and ankle joints are designed with one degree of freedom. Each joint of the HLLE is designed with mechanical limits, and 6061-T6 is used as the main construction material of the HLLE. In the ADAMS simulations, the spline curves of angle versus time at v₃ = 1.147 m/s are used as joint data of the human–machine coupled model. The average moments of 78.518 and 29.622 Nm are obtained for the right hip and knee joints, respectively. The foot member of the HLLE is subjected to a maximum impact force of 2758.233 N at the right foot. The 3D HLLE model is analyzed in the standing, swinging, single limb support, and double limb support phases by the finite element analysis method using Ansys Workbench software. The maximum stress values in the standing, swinging, single limb support, and double limb support phases are determined to be 12.7%, 23.1%, 4.5%, and 51.8% of the yield strength of the material at the corresponding place, respectively. The stress distribution results show that the selected material and designed structure of the HLLE can satisfy the strength requirements. The first-order intrinsic frequencies in the standing phase and double limb support phases are 18.239 and 23.086 Hz, respectively.

3. An FPGA-based control system is designed, and its input is the pressure between the exoskeleton and the limb, while its output is the servo angle. The experiments with the subjects walking with a weight of 20 kg without and with the lower limb exoskeleton are conducted. The EMG signal acquisition devices attached to the subjects’ thighs and shanks are used to collect data for analysis. The amplitude value variation range of the subjects wearing the HLLE is compared with that of the subjects not wearing the HLLE. For the former, the ranges of amplitude changes at the right thigh, right shank, left thigh, and left shank are 15.5%, 41.6%, 40.8%, and 37.7% of those of the latter, respectively. Thus, it is verified that the HLLE has a booster effect during human weight-bearing walking.

The following aspects of the HLLE should be improved in future studies: (1) Degrees of freedom in the coronal and horizontal planes should be added to the design of the mechanical mechanism in the ankle joint. These additional degrees of freedom will allow the HLLE ankle joint to better adapt to human ankle motion. (2) The position of the joint centers of the HLLE can become misaligned with the position of the joint centers of the human body during work; therefore, adding a function for the joint center of the HLLE to automatically follow the position of the joint center of the human body should be a priority for future research. Since the HLLE itself has a certain weight and is fixed to the human body by a nylon bandage, there will be relative sliding between the subject and the machine when the subject walks. This will cause the subject to feel slight discomfort at the point where the HLLE contacts the body. (3) Since the current design is only suitable for special individuals, in future research, it is hoped that the HLLE can be used by healthy young people of different body shapes.